When Markets Lose Dimensions: Foldability, Diversification Runs, and the Public Good of Risk Transfer

Financial crises do not merely move prices, raise volatility, or increase correlations. They can destroy market dimensions. We study the effective dimensionality of market risk, measured by the participation ratio of the covariance spectrum, and identify it as a public good: it is shared by all market participants, non-rival in normal use, congestible under stress, and underpriced relative to its social shadow value. When investors deleverage under Value-at-Risk or margin constraints, fire-sale feedback can collapse a high-dimensional covariance structure into a near one-factor market. We formalize this mechanism as a diversification run, the asset-side analogue of a Diamond-Dybvig bank run. The diversified equilibrium is Pareto-superior, but the collapsed equilibrium is individually rational when others deleverage. Under private signals of the distance to the fold, a global-games refinement selects a unique threshold equilibrium — the run occurs if and only if the market is close enough to the fold — so the mechanism is not a story of free belief indeterminacy. Competitive equilibrium can therefore destroy the market dimensionality required for welfare optimality. A formally verified proof suite supports the mechanism: its derived core is the saddle-node collapse, the foldability threshold, the microfounded welfare ordering, and the global-games threshold; its remaining layers verify the public-good, run-theoretic, and policy implications conditional on the stated assumptions. The mechanism's sharpest testable prediction is a pre-crisis foldability signal: dimensions classified as foldable before a crisis are precisely those that lose eigenvalue share when the crisis becomes a dimension-collapse event. In an empirical-first master design using archived WIKI stock-level data for pre-2018 crises and a modern public stock panel for post-2018 events, the foldability ordering is correct in all four qualified dimension-collapse events (LTCM 1998, the GFC, COVID 2020, and the 2022 tightening episode; sign test p=0.0625), and the event-level foldable-minus-immune share gap is positive in every case (mean +0.027, one-sample t-test p\approx 0.07). Adding three independent stock-level international events (the 2011 European sovereign crisis, the 2015 China devaluation, and the 2018 Italian sovereign-spread crisis, from regional large-cap panels under the identical method) raises the event-level gap test to seven independent events, where it is significant (t=3.86, p=0.008 two-sided, seven of seven positive). The pooled spectral-dimension foldability coefficient is strongly negative; because eigen-dimensions within an event are not independent, we judge its significance on an event-clustered standard error and on the event-level gap test rather than on the nominal eigen-level p-value. Maturity: Draft. Part of The Latent research program. Related papers in this program: Universal.